Lorde is mesmerising fans - and critics - during her sold-out North American tour.

The 17-year-old Kiwi pop sensation told Twitter followers that the 16-date tour sold out on January 13, less than a month after it was announced and a fortnight before she won two Grammy awards for her song Royals.

The tour began March 3 in Texas, with dates in New York, Toronto, Chicago, Boston and Detroit, and will finish March 26 in California.

In a review of her opening night in Austin, Rolling Stone magazine said the "young woman" seemed comfortable and in control on stage.

The Austin Chronicle described Lorde as "Pop's majesty", her lyrics as beyond her years, and thanked God for her "honesty".

"Amazing that a girl born in 1996 wrote one of the best songs about aging, but we've already come to expect just such posture from Lorde."

Praising instead her youth and innocence, the paper said Lorde's music was a "relief" from typical pop trappings of the good life, the Houstonia said.

"Her music is shockingly devoid of the sexualised femininity and vacuous excess that we have come to expect from celebrities, and full instead of mundanities like driving around aimlessly listening to pop music and hanging out with friends."

On Monday, before her first New York show at the Roseland Ballroom, Lorde posted a video on Instagram of her breathing into an oxygen mask, with the comment: "typical .. sick before my NYC shows! vaporizerrrrr time".

Judging from more positive reviews, she made a full recovery.

New York media appeared to embrace Lorde's characteristic dance style - MTV said "the music was her puppeteer" and the New York Times said it completed her implied "alterity".

"Lorde moves in tiny convulsions, arms thrusting out at jagged angles. It is convincing, awkward movement, and completes an air of unfiltered reverie," the paper said.

There was praise for the set's simplicity and minimalism and New York media applauded her voice.

"Her voice was resonant and a little husky, and on long notes you could almost hear the muscles work," the New York Times said.

The ballroom venue seemed to suit the anti-glitterati singer. Roseland is general admission only, meaning there are no seats. Face-price tickets allows door entry, and from there individuals work their way up to the front of the house.

Lorde will follow her tour with performances at major music festivals, including Lollapalooza in Chile and Brazil, and Coachella in California.